CHAPTER 5
Solution’s for CHEMICAL REACTION ENGINEERING
BY-OCTAVE LVENSPIL
CHAPTER 5
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Problem 5.1 (p. 113)
reaction 2 A →R + 2 S with kinetic
unknown. If required a space velocity of 1 min-1 to achieve
90% conversion of A in a plug flow reactor, find the Consider the gas phase
Space and time corresponding mean residence time of the fluid
in the plug flow reactor
soln
If the system is of constant density and residence time time
space are equal, but in this case the system is of variable density
because the flow rate varies during the reaction, since it is a
gaseous and varies the total number of moles.
Conclusion
No one can calculate the mean residence time of the fluid with the data
available
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Problem 5.2 (p. 113)
In a batch reactor operated isothermally reached 70%
conversion of liquid reagent in 13 min. What is space weather
required to perform this operation in a plug flow reactor and
one complete mix?
because the system is constant density so you (is liquid)
Can not be calculated τ, or s for mixed reactor because
kinetics known.
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Problem 5.3 (p. 113)
An aqueous stream of monomer A (1 mol / L, 4 L / min) enters a
complete mixing reactor 2 where L is the radiated and polymerizes
follows
A→R→ S → T ........
In the output current CA = 0.01 mol / L and for a particular product W
must be CW = 0.0002 mol / L. Find reaction rate of A and
W
Solution
A→R
R + A→S
S + A→T
T + A→U
U + A→V
V + A→W
Assuming that the reactions are elementary
-RA = k1CA + k2 + k3 CA CA CR CS CT + CA + k4 k5 + k6 CA CA CU CV
rW = CV + k6 k7 CA CA CW
There are 7 kinetic constants involved, so I require at least 8 points
experimental to calculate the numerical value of the constants.
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Problem 5.4 (p. 113)
It is planning to replace a mixed reactor with one that
has twice the volume. For the same feed rate and the
same aqueous feed (10 mol of A / L), find the new conversion. The
The reaction kinetics are represented by
CA1-rA = k, 5
A→R
The actual conversion is 70%.
Solution
6
Calculated
4
Correct
M
2
0
0.74
0.76
0.78
0.8
0.82
Conversion
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Problem 5.5 (p. 113)
An aqueous feed A and B (400 L / min, 100 mmol / L of A, 200
mmol / L of B) will be converted to product in a flow reactor
piston. The kinetics of the reaction is represented by:
CA-CB rA = 200 mol / L min
A + B→R
Find reactor volume required to achieve 99.9%
A product conversion in
Solution
Constant density liquid system
-
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Problem 5.6 (p. 113)
A plug flow reactor (2 m3) processes an aqueous feed (100
L / min) containing a reagent A (CA0 = 100 mmol / L). This reaction is
reversible and is represented by:
A
R
-RA = 0.04 min-1CA - 0.01 min-1 CR
Find first equilibrium constant and after the reactor the conversion
Solution
System fluid density is constant because
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Problem 5.7 (p. 114)
The gas coming out of a nuclear reactor containing a full range of
radioactive traces, the conflict being the Xe-133 (mean
life = 5.2 days) This gas flows continuously through a tank with a
high retention, with residence time of 30 days, which may be
assume that the contents are well mixed. Find activity fraction
that is removed in the tank
Solution
Assuming that the reaction is of constant density and that is first
order can be calculated from the kinetic constant through time
life
For mixed reactor
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Problem 5.8 (p. 114)
A mixed reactor (2 m3) processes an aqueous feed
(100 L / min) containing a reagent A (CA0 = 100 mmol / L). This reaction
is reversible and is represented by:
A
R
-RA = 0.04 min-1CA - 0.01 min-1 CR
What is the equilibrium conversion and the actual conversion of the reactor?
Solution
System fluid density is constant because
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Problem 5.9 (p. 114)
A specific enzyme catalyzes the fermentation of A.
Find the volume of the plug flow reactor required for 95% of
conversion of reactant A (CA0 = 2 mol / L) at a given concentration of
enzyme. Fermentation kinetics of this enzyme concentration
is given by:
enzyme
A → R
CA-rA = 0.1 / (1 + 0.5 CA)
Solution
System constant density because 1 mol of A yields 1 mol of R
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Problem 5.10 (p.114)
In a plug flow reactor a gaseous feed of pure (2
mol / L, 100 mol / min) decomposes to give a variety of products.
The kinetics of the reaction is represented by
A→2.5 products
-RA = 10 min-1 CA
Find expected conversion reactor 22 L
Solution
System variable density varies because Ftotal, which causes the flow
volume varies
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Problem 5.11 (p. 114)
The enzyme catalyzes the fermentation E substrate A (reactive),
obtaining R. Find size required mixed reactor
for 95% conversion of a feed stream (25 L / min)
reagent (2 mol / L) and enzyme. Fermentation kinetics at this
enzyme concentration is given by
enzyme
A → R
CA-rA = 0.1 / (1 + 0.5 CA)
Solution
Constant density System
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Problem 5.12 (p.114)
An aqueous solution (400 L / min, to 100 mmol / L, 200 mol of B / L) will
be converted to product in a mixed reactor. The kinetics of
the reaction is represented by
A + B→R
CA-CB rA = 200 mol / L min
Find reactor volume required to achieve 90% conversion
Solution
System fluid density is constant because
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Problem 5.13 (p. 115)
At 650 ° C the vapor decomposes as follows PH3
4 PH3 →P4 (g) +6 H2
-RPH3 = 10 h-1 CPH3
What size of plug flow reactor operating at 649 ° C and 11.4 atm
required to achieve 75% conversion of 10 mol / H PH3 having
2/3 of PH3 y1 / 3 inert?
Solution
System variable density varies because it is gaseous and Ftotal, which
causes the volumetric flow varies
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Problem 5.14 (p. 115)
A gas stream of pure reagent A (CA0 = 660 mmol / L) enters a
plug flow reactor at a rate FA0 = 540 mmol / min and polymerized
as follows
3A→R
-RA = 54 mmol / L min
How big should the reactor to CAF = 330 mmol / L?
Solution
System variable density because it varies Ftotal gas and as the flow
volume also vary
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Problem 5.15 (p. 115)
A gaseous feed of pure A (1 mol / L) enters reactor
complete mixture (2 L) and reacts as follows:
2A→R
CA2-rA = 0.05 mol / L s
Find feed rate (L / min) to give a concentration of
CAf output = 0.5 mol / L
Solution
System variable density as it is gaseous and Ftotal varies during
During the reaction, the volumetric flow varies
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Problem 5.16 (p. 115)
The gaseous reagent is decomposed as follows
A→3R
-RA = 0.6 min-1 CA
Find A conversion is obtained in a complete mixing reactor
of 1 m3 which is fed with a stream containing 50% A and 50%
of inert (v0 = 180 L / min, CA0 = 300 mmol / L)
Solution
System variable density as it is gaseous and Ftotal varies during
During the reaction, the volumetric flow varies
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Problem 5.17 (p. 115)
A mixture of ozone 20% - 80% air at 1.5 atm and 95 ° C passes at a
rate of 1 L / s through a plug flow reactor. Under these
conditions decomposes ozone by reaction homogeneous
-RA = k Coz2
k = 0.05 L / mol s
2 O3 →3 O2
What size
decomposition?
reactor
is
requires
for
achieve
50
%
of
Solution
The rate of reaction is second order and the system of density
Yavariable design equation and varies because Ftotal is
gaseous.
integrated in the text for this case.
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Problem 5.18 (p. 116)
An aqueous feed containing A (1 mol / L) is processed in a
plug flow reactor 2 L (2 A →R, CA2-rA = 0.05 mol / L s). Find the
The outlet concentration for a feed rate of 0.5
L / min
Solution
The system is liquid, so it is of constant density and εA =0
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Problem 5.19 (p. 116)
Is fed to a complete mixing reactor 1 a gas stream L
A pure approximately 3 atm and 30 ° C (120 mmol / L). There are
decomposed and the concentration of A in the output is measured for each
flow rate. From the data the following equation Find
represents the decomposition rate of A. Suppose that only
A concentration affects the rate of reaction
v0 (L / min)
CA (mmol / L)
0.06
30
0.48
60
1.5
80
8.1
105
Solution
The system is of variable density varies because it is gaseous and F total
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A→3R
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Problem 5.20 (p. 116)
You are using a mixed reactor to determine the
reaction kinetics whose stoichiometry is A →R. For this different
flow of an aqueous solution containing 100 mmol / L of A are
fed to a reactor of 1 L and for each run the concentration of A
output is recorded. Find the equation representing the speed
following. Assume that only the reagent A affects the speed of
reaction
v (L / min)
CA (mmol / L)
4
6
20
24
50
Solution
The system is fluid density is constant because
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Problem 5.21 (p.116)
It is planning to operate a batch reactor to convert A into R
by reaction in liquid phase with the stoichiometry A →R, whose
reaction rate is shown in the following table
CA
(Mol / L)
-RA
(Mol / Lmin)
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
1.0
1.3
2.0
0.1
0.3
0.5
0.6
0.5
0.25
0.1
0.06
005
0.045
0.042
How long must react each tuned to the concentration falls
from CA0 = 1.3 mol / L to CAF = 0.3 mol / L?
Solution
System fluid density is constant because
-RA is plotted vs CA to complete the data between CA = CA = 0.8 to 1.3
mol / L. Axis is used to facilitate the representation semilog
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Problem 5.22 (p. 116)
For the reaction of 5.21 problem, what size flow reactor
the piston is required for 80% conversion of a stream of 1000
A mol / h with CA0 = 1.5 mol / L
Solution
The density is constant and CA0 CAF = (1 - XA) = 1.5 (1 -0.8) = 0.3 mol / L
Chart values are taken from problem 5.21. Reproduced extended the
necessary part of the graph
0.1
0
0.5
1
1.5
2
Reaction
rate
Concentration A
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2.5
Problem 5.23 (p. 117)
a) For the reaction of 5.21 problem, what size CSTR
Full required to obtain 75% conversion of
stream A 1000 mol / h with CA0 = 1.2 mol / L
b) Repeat part a) with the modification that the power is
double, or A 2000 mol / h with CA0 = 1.2 mol / L
c) Repeat part a) with the modification that CA0 = 2.4 mol / L,
1000 mol treating A / h and CAF = 0.3 mol / L
Solution
b)
Assuming that the volume is still 1500 L and that what varies is XA
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correct
calculated
XAF /-RAF never going to be 0.75,
said physically with τ
not occur as small
reaction
Assuming XA = 0.75 and the volume required varies
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Problem 5.24 (p. 117)
A gaseous hydrocarbon of high molecular weight is fed a continuously mixed reactor
which is heated to high temperatures to cause thermal cracking (homogeneous reaction
gaseous) materials of lower molecular weight, collectively called
R using approximate stoichiometry A →5 R. Changing
feed rate is obtained different extensions cracking
as shown
FA0 (mmol / h)
CAs (mmol / L)
300
16
1000
30
3000
50
The vacuum inside the reactor volume is 0.1 L and temperature
A feed concentration is CA0 = 100 mmol / L. Find the equation
which represents the cracking reaction
Solution
System variable density varies because it is gaseous and Ftotal
Draw a graph of rate of reaction vs concentration of A
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5000
60
Problem 5.25 (p. 117)
The aqueous phase decomposition of A is studied in a reactor
thorough mixing. The results in the table were obtained P.5.25
steady state runs. What residence time required for
obtain 75% conversion of reagent feeding with CA0 = 0.8
mol / L
CAe
CAs
2.00
0.65
2.00
0.92
2.00
1.00
1.00
0.56
1.00
0.37
0.48
0.42
0.48
0.28
0.48
0.20
t (S)
300
240
250
110
360
24
200
560
Solution
The system density is constant, so
These values are plotted for values-rA vs CA necessary
Reaction
rate
Concentration A
.
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Problem 5.26
Repeat the previous problem, but for a completely mixed reactor
Solution
=
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Problem 5.28 (p. 118)
In a batch reactor operating at constant volume and 100 ° C.
The following data were obtained from the decomposition of gaseous reactant A
t (s)
pA (atm)
0
1.00
20
0.80
40
0.68
60
0.56
80
0.45
100
0.37
140
0.25
200
0.14
260
0.08
The stoichiometry of the reaction is 2 to →R + S
What size of plug flow reactor (in L) can operate at 1 atm
A treat 100 mol / h in a stream containing 20% inerts in
to obtain 95% conversion of A
Solution
The system is of constant density, both in the batch reactor as
in the plug flow because Ftotal = Ntotal = constant
-rA =KC
n
If first-order
kt = - ln (1-X A )
PA/pA0 is plotted vs. t gives a straight line and if it means 1st order
1
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330
0.04
420
0.02
Then the reaction is first order
For plug flow reactor using equation 5.23 (p. 103)
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Problem 5.29 (p. 119)
Repeat the previous problem, but for a completely mixed reactor
Solution
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